Download App

Circles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCircles1 Mark
Question
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
✓

Answer

False.
Consider any point P external to a circle away from O . Now, draw tangent PA on the circle. Clearly, $PA > r [\because P$ is external to circle and P is at sufficient distance] Now, again consider any point $P_1$ on the tangent $A P$ very near to contact point $A$ of tangent $P A, P_1 A<A O S o$, it is clear that the length of the tangent $P A$ and $P_1 A$ are greater and smaller respectively than radius $O A$. Hence, the length of the tangent from an external point of a circle may or may not be greater than the radius of the circle. Hence, the given statment is false.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from Circles→Circles — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Write ‘True’ or ‘False’ and justify your answer.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.
→
Write ‘True’ or ‘False’ and justify your answer.
$\sqrt{(1-\cos^2\theta)\sec^2\theta}=\tan\theta$
→
Write ‘True’ or ‘False’ and justify your answer.
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then $\text{OP}=\text{a}\sqrt{3}.$
→
State whether the following statements are true or false. Justify your answer.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(-1, 1) and B(3, 3).
→
Write ‘True’ or ‘False’ and justify your answer in the following:
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
→
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point P on a circle with centre O is always less than OP.
→
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false Why?
→
Write 'True' or 'False' and justify your answer.
If $\cos A+\cos ^2 A=1$, then $\sin ^2 A+\sin ^4 A=1$
→
Two numbers have 12 as their HCF and 350 as their LCM .
→
Write ‘True’ or ‘False’ and justify your answer.
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
→